Up to the early twentieth century, knowledge of materials with limited coefficients of expansion was essentially limited to naturally occurring materials, elements or compounds. The advent of atomic science in the early twentieth century brought with it both an emergent understanding of materials at atomic scale and the need for measurement several magnitudes of precision greater than had previously been known. This in turn led to research for new materials, compounds or alloys, which exhibited limited thermal expansion for the purpose of building measuring instruments.
One newly discovered material was the ferro-nickel alloy eventually named Invar, which was the work of several physicists, culminating in the limited thermal expansion alloy work of Charles Édouard Guillaume. The isotropic FeNi alloy produced has a low thermal linear expansion rate. Its derivative alloys can exhibit an abnormal (i.e. positive) thermal evolution of elastic modulus; that is, an increase in elastic modulus with a rise in temperature. The drawback of these alloys in the modern world (especially their use in balance springs for precision instruments) is their sensitivity to magnetic fields and a change from abnormal (i.e. positive) thermal evolution of elastic modulus to normal (i.e. negative) thermal evolution of elastic modulus in the ambient temperature range.
As well as discovering that the inflection of the curve showing thermal evolution of elastic modulus (i.e. the transition between abnormal and normal behaviour) of the FeNi alloy occurs at lower than blood temperature, the present inventor has investigated and successfully applied the use of new and non-magnetically sensitive materials to address problems arising from use of the FeNi alloy in balance springs for mechanical oscillator systems (such as for a horological mechanism, e.g. mechanical watch).
In general, the formula for timekeeping changes (U) consequent upon a rise in temperature of 1° C. in a watch's mechanical oscillator system, where the thermal expansion coefficient of the balance wheel is represented by the term α1, the thermal expansion coefficient of the balance spring by α2, the elastic modulus Young's modulus) by the term E, and the change in E over the 1° C. temperature rise by δE, is:
  U  =            α      1        -                  3        ⁢                  α          2                    2        -                            δ          ⁢                                          ⁢          E                          2          ⁢          E                    .      
U can be made to tend to zero when suitable values of α1, α2 and E are selected by careful choice of appropriate materials. It can be expedient to derive the solution to this equation in the material of the balance spring if possible by focusing on the terms α2 and
            δ      ⁢                          ⁢      E              2      ⁢      E        .In other words, if the dimensional changes and elastic modulus can be controlled and equated with a given (i.e. fixed or otherwise predetermined) balance wheel thermal expansion rate, the total number of industrial processes and parts required to produce the oscillator can be reduced.
In WO 2004/008259 the present inventor disclosed using the anisotropy of certain balance spring materials such that the length of the spring did not increase with a rise in temperature whilst the width and height of the spring did increase with the same temperature rise. Such balance springs were disclosed for use in mechanical oscillator systems for horological instruments, e.g. mechanical watches. The thermal evolution of the balance spring material disclosed in this application can allow a very close rate in watches to be obtained and maintained using non-magnetic materials.
Separately, EP 1 422 436 discloses a watch balance spring material having an abnormal thermal evolution of elastic modulus comprising an isotropic material having a normal thermal evolution of elastic modulus coated with a material having an abnormal thermal evolution of elastic modulus. However, although a change in the sign of the thermal evolution of elastic modulus has been found, consistent manufacturing tolerance has been difficult to achieve and the resultant stiffening of the material has required further compensatory measures.